A174646 Number of ways to place 7 nonattacking amazons (superqueens) on a 7 X n board.

0, 0, 0, 0, 0, 0, 0, 0, 2, 100, 908, 4872, 19818, 66864, 193926, 498924, 1165544, 2517036, 5089430, 9731908, 17735888, 30999920, 52234274, 85210284, 135059570, 208627984, 314889330, 465423908, 674966914, 962031720, 1349613074

Offset

1,9

Comments

An amazon (superqueen) moves like a queen and a knight.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

The Oprisch Family Web Site

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Formula

G.f.: 2*x^9 * (8*x^22 - 4*x^21 - 9*x^20 + 102*x^18 - 138*x^17 + 29*x^16 + 592*x^15 - 1610*x^14 + 2772*x^13 - 3091*x^12 + 3178*x^11 - 2049*x^10 + 1312*x^9 - 625*x^8 + 1438*x^7 - 449*x^6 + 388*x^5 + 403*x^4 + 148*x^3 + 82*x^2 + 42*x + 1)/(x-1)^8.

Explicit formula: a(n) = n^7 - 85n^6 + 3329n^5 - 77911n^4 + 1175240n^3 - 11392990n^2 + 65448630n -171006180, n>=24.

Mathematica

CoefficientList[Series[2 x^8 (8 x^22 - 4 x^21 - 9 x^20 + 102 x^18 - 138 x^17 + 29 x^16 + 592 x^15 - 1610 x^14 + 2772 x^13 - 3091 x^12 + 3178 x^11 - 2049 x^10 + 1312 x^9 - 625 x^8 + 1438 x^7 - 449 x^6 + 388 x^5 + 403 x^4 + 148 x^3 + 82 x^2 + 42 x + 1) / (x - 1)^8, {x, 0, 50}], x] (* Vincenzo Librandi, May 30 2013 *)

Crossrefs

Cf. A174642, A174644, A174645.

Sequence in context: A374397 A202945 A230816 * A092699 A121975 A102188

Adjacent sequences: A174643 A174644 A174645 * A174647 A174648 A174649

Keyword

nonn,easy

Author

Vaclav Kotesovec, Mar 25 2010

Status

approved